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We consider closed, Weyl-transitive groups of automorphisms of thickbuildings. For each element of such a group, we derive a combinatorial formulafor its scale and establish the existence of a tidy subgroup for it that equalsthe stabilizer of a simplex. Simplices whose stabilizers are tidy for someelement of the group are characterized in terms of the minimal set of theisometry induced by the element on the Davis-realisation of the building and interms of the Weyl-distance between them and their image. We use our results toderive some topological properties of closed, Weyl-transitive groups ofautomorphisms.

Scale and tidy subgroups for Weyl-transitive automorphism groups of buildings